Non-Hermitian Computers Need No Complex Numbers
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918526741118976 |
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| author | Zhang, Qi |
| author_facet | Zhang, Qi |
| contents | In traditional quantum computing, it has been established that real quantum computation augmented with non-Clifford gates is as powerful as universal quantum computation. Here we investigate this phenomenon in the non-Hermitian setting. We show that a non-Hermitian quantum computer equipped with the real gate set ${H, \text{CCNOT}, G}$, where $G = \operatorname{diag}(g^{-1}, g)$ with $g > 0$ and $g \neq 1$, can solve problems in $\text{P}^{\sharp\text{P}}$ in polynomial time, matching the capability of its universal non-Hermitian counterpart ${H, T, \text{CNOT}, G}$. This demonstrates that non-unitarity, rather than universality, is the essential resource, and that complex numbers are unnecessary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Computers Need No Complex Numbers Zhang, Qi Quantum Physics In traditional quantum computing, it has been established that real quantum computation augmented with non-Clifford gates is as powerful as universal quantum computation. Here we investigate this phenomenon in the non-Hermitian setting. We show that a non-Hermitian quantum computer equipped with the real gate set ${H, \text{CCNOT}, G}$, where $G = \operatorname{diag}(g^{-1}, g)$ with $g > 0$ and $g \neq 1$, can solve problems in $\text{P}^{\sharp\text{P}}$ in polynomial time, matching the capability of its universal non-Hermitian counterpart ${H, T, \text{CNOT}, G}$. This demonstrates that non-unitarity, rather than universality, is the essential resource, and that complex numbers are unnecessary. |
| title | Non-Hermitian Computers Need No Complex Numbers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.28152 |